Collection or fix-up?
This is a collection of stories turned into a fix-up novel by adding some introductory material to each story. It's hard to know whether to approach it as a collection or as a novel. I'm choosing to see it as a single sweeping story told in parts, so I'm categorizing it as a novel. That may be the wrong choice.

The broad sweep
The overarching story reminds me of Olaf Stapledon's Last and First Men, with maybe a hint of Blish's Cities in Flight. It's a narrative that gives us slices from the history of the entirety of mankind's existence. We start in our near future and continue into the inconceivable distant future and the eventual end of mankind. I enjoyed the first three stories, but after that it got really dumb and metaphysical and I hated it.

• The War Millennia - Out of Reach: Floyd Milton takes a portmatter unit to the Solite home world, and discovers why the Solites have never revealed the location of their world, and why they are so interested in collecting samples of Earth's flora and fauna. Solite is Earth in the future after a "supreme catastrophe" wiped out most life forms on the planet.
• The Sterile Millennia - All the World's Tears: J. Smithlao is a psychodynamician, whose job is to rouse men to anger—a hate-brace—which is the only way to fan the last sparks of ambition in mankind. In this dying world humanity is counted in the hundreds and humans prefer complete isolation and to never see, much less touch another human being. The species is kept alive only by the efforts of the Mating Center. Smithlao observes as one Ployploy (rejected by the Mating Center as unfit) encourages the advances of a wild man—with deadly consequences. She explodes when touched. The Mating Center implanted that response into her cells as a safeguard.
• The Robot Millennia - Who Can Replace a Man?: When the last man dies, the robots on the farm talk amongst themselves and try to decide what to do. The robots argue a lot, but usually defer to whoever has the highest class brain. Eventually they make their way to the mountains and find a lone surviving man.
• The Mingled Millennia - Blighted Profile: An inscrutable story, set in the Solite era.
• The Dark Millennia - O Ishrail!: A man calling himself Ishrail shows up and claims to be an exiled admiral from a galaxy-wide war that, conveniently, Earth knows nothing about. Will he be believed?
• The Star Millennia - Incentive: Apparently yes, Ishrail was believed. Later, the Galactic Council votes to admit Earth into the galactic Federation. However, Earth is skeptical. Galactic Minister Jandanagger Laterobinson makes his case to Isolationist representative Farro Westerby: by adopting the galactic language Galingua, the people of Earth can unlock the secrets of the universe—including interstellar travel by language rather than by cumbersome spaceships. This is so, so dumb, and I hate it so much. Also, Earth must consent to being renamed Yinnisfar. So dumb.
• The Mutant Millennia - Gene-Hive: An accidental mutation catapults mankind into a new stage of evolution: a shape-shifting hive of cellular goo that can be anyone and everyone and everything. The mutant cells try to absorb all life in the galaxy, but are eventually defeated by the forces of free men who wish to retain their individual existence rather than become part of a hive mind and body. So dumb.
• The Megalopolis Millennia - Secret of a Mighty City: An aspiring film-maker (well, solid-maker because this is the future and we're doing 3D TV) pitches a documentary about the real, authentic underbelly of the big city. What is this junk?
• The Ultimate Millennia - Visiting Amoeba: Our galaxy is running down. Whereas in our galaxy, man was the pinnacle of evolution, in the next galaxy man is just the beginning: the most primitive amoeba form from which higher levels will evolve. This was not worth my time.